Q48E TRUE OR FALSEIf A=[1221]then the... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 5: Q48E (page 264)

TRUE OR FALSE
If $A = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ then the matrix Q in the QR factorization of A is a rotation matrix.

Short Answer

Expert verified

The given statement is false.

Step by step solution

Given information

Consider the given statement as follows.

If $A = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ , then matrix Q in the QR factorization of A is a rotation matrix.

Check the given statement

Consider the given matrix.

$A = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$

To find the QR factorization of role="math" localid="1659626163025" $A = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$

A direct computation or geometric approach shows that $Q = \frac{1}{\sqrt{5}} [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ represents a matrix, not a rotation matrix.

This can be obtained geometrically as the vector perpendicular to the vector $[\begin{matrix} 1 \\ 2 \end{matrix}]$ is either $[\begin{matrix} 2 \\ 1 \end{matrix}]$ or $[\begin{matrix} - 2 \\ 1 \end{matrix}]$ .

Hence, the given statement 鈥淭he matrix Q in the QR factorization of A is a rotation matrix is false鈥�.

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91影视

TRUE OR FALSE
If $A = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ then the matrix Q in the QR factorization of A is a rotation matrix.

Short Answer

Step by step solution

Given information

Check the given statement

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91影视

TRUE OR FALSEIf A=[1221]then the matrix Q in the QR factorization of A is a rotation matrix.

Short Answer

Step by step solution

Given information

Check the given statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

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Applied Mathematics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

TRUE OR FALSE
If $A = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ then the matrix Q in the QR factorization of A is a rotation matrix.